Insurance Commons^™

Credibility Theory And Geometry, Elias S.W. Shiu, Fuk Yum Sing

Journal of Actuarial Practice (1993–2006)

We present a geometric approach to studying greatest accuracy credibility theory. Our main tool is the concept of orthogonal projections. We show, for example, that to determine the Buhlmann credibility premium is to find the coefficients of the minimum-norm vector in an affine space spanned by certain orthogonal random variables. Our approach is illustrated by deriving various common credibility formulas. Several equivalent forms of the credibility factor Z are derived by means of similar triangles.

Product Innovation In Financial Services: A Survey, Christopher O'Brien

Journal of Actuarial Practice (1993–2006)

This paper considers product innovation in insurance and other financial services, an area where actuaries have an important role. It considers the proposition that there is no unique formula for success and that what works well in one situation may not work well in another. It first examines the sources of ideas for new products and, in particular, the role played by consumers, which is generally regarded as weak. It then looks at how ideas are implemented, with particular importance attributed to cross-functional teams and the formality of the product development process. Then it considers how success is measured (with …

Estimation Of Complete Period Life Tables For Singaporeans, Siu-Hang Li, Wai-Sum Chan

Journal of Actuarial Practice (1993–2006)

Complete period life tables, with death rates for every year of age, are not available in Singapore. This study constructs such tables for Singaporeans from the limited mortality information contained in the abridged life tables provided by the Singapore Department of Statistics. We find that linear interpolation, Whittaker graduation, and the Coale-Kisker method together can generate complete life tables that are smooth and continuous. The validity of the complete life tables generated by our method is further confirmed by (1) comparing the life expectancies calculated from our estimated life tables with those provided by the Singapore Department of Statistics, and …

Beware Of The Ides Of March: The Demise Of Hih Insurance, Bonnie Buchanan, Tom Arnold, Lance Nail

Finance Faculty Publications

Despite differences in corporate governance systems in the United States and Australia, the corporate governance failures that led to each country’s largest bankruptcy are strikingly similar. WorldCom in the United States and HIH Insurance in Australia were both created by a rapid series of major acquisitions, failed after their last major acquisitions, and attempted to hide their declining performance with aggressive and/or fraudulent accounting practices. In this paper we present a clinical examination of the corporate governance failures that led to the demise of HIH Insurance and show that corporate governance failures are not endemic to the existing corporate governance …

Sampling Concepts, Paul Boyd, Ph.D.

MBA Faculty Conference Papers & Journal Articles

The usefulness of any research is dependent upon how well the group studied represents the group about which decisions are to be made or conclusions drawn. That is, it depends upon how well the sample reflects relevant characteristics of the population. When it is possible to study every member of that group there is no problem, for on these occasions we can easily calculate the exact attribute (parameter) of interest for our population.

For example, if we were interested in determining the average number of gallons of gasoline sold to customers at our service station yesterday, we …

Journal Of Actuarial Practice, Volume 10, 2002, Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

ARTICLES

Communicating Effectively with Words, Numbers, and Pictures: Drawing on Experience • Karolina Duklan and Michael A. Martin

Unearned Premiums and Deferred Policy Acquisition Expenses in Automobile Extended Warranty Insurance • Joseph Cheng

Can Utility Maximization Models Assist With Retirement Planning? • Zaki Khorasanee

Dynamic Funding and Investment Strategy for Defined Benefit Pension Schemes: A Model Incorporating Asset-Liability Matching Criteria • Shih-Chieh Chang, Cheng-Hsien Tsai, Chia-Jung Tien, and Chang- Ye Tu

Model Risk and Surplus Management Under a Stochastic Interest Rate Process •Jennifer L. Wang and Rachel J. Huang

Some Comments on the Pricing of an Exotic Excess of …

Improving Mortality: A Rule Of Thumb And Regulatory Tool, John H. Pollard

Journal of Actuarial Practice (1993–2006)

We develop a simple exact formula for determining cohort life expectancies under constant continuous uniform improvement in mortality using only a cross-sectional (period) Gompertz life table for the lives concerned and a simple approximation applicable to all life tables. The present values of annuities for such lives can be determined simply and accurately across the whole age span.

Modeling Size-Of-Loss Distributions For Exact Data In Winbugs, David P.M. Scollnik

Journal of Actuarial Practice (1993–2006)

This paper discusses how the statistical software WinBUGS can be used to implement a Bayesian analysis of several popular severity models applied to exact size-of-Ioss data. The particular models targeted are the gamma, inverse gamma, loggamma, lognormal, (two-parameter) Pareto, inverse (two-parameter) Pareto, Weibull, and inverse Weibull distributions. It is possible to implement additional size-of-Ioss models (including those for truncated data) using methods analogous to those described herein.

Model Risks And Surplus Management Under A Stochastic Interest Rate Process, Jennifer L. Wang, Rachel J. Huang

Journal of Actuarial Practice (1993–2006)

This paper uses simulations to explore the effects of incorrectly identifying the underlying interest rate process on assets, liabilities, and surplus levels. We show that mismodeling the interest rate (called model risk) could not only lead to a misstatement of the company's surplus, but could also cause a mismatch between the company's assets and liabilities. Our simulations demonstrate that three aspects of interest rates affect model risk: (i) volatility, (ii) level of long-term interest rate, and (iii) the speed at which the drift rate adjusts. We conclude that asset-liability managers should not ignore the impact of the model risks, regardless …

Unearned Premiums And Deferred Policy Acquisition Expenses In Automobile Extended Warranty Insurance, Joseph Cheng

Journal of Actuarial Practice (1993–2006)

A prorata formula is commonly used to calculate unearned premium reserves in property-casualty insurance. I believe, however, that an exposure-adjusted formula is more appropriate in automobile extended warranties. This paper describes the exposure-adjusted approach to calculate the unearned premium reserves of an automobile extended warranty insurance program, to test the adequacy of the calculated reserves, and to determine the allowable deferred policy acquisition expenses from an insurance company's perspective.

Journal Of Actuarial Practice Volume 10 (2002) -- Contents And Masthead

Journal of Actuarial Practice (1993–2006)

Contents

Editorial Policy: Topics suitable for this journal include AIDS, annuity products, asset-liability matching, cash-flow testing, casualty rate making, credibility theory, credit insurance, disability insurance, expense analysis, experience studies, FASB issues, financial reporting, group insurance, health insurance, individual risk taking, insurance regulations, international issues, investments, liability insurance, loss reserves, marketing, pensions, pricing issues, product development, reinsurance, reserving issues, risk-based capital, risk theory, social insurance, solvency issues, taxation, valuation issues, and workers' compensation

Review Process

Editor - Colin Ramsay, University of Nebraska

Associate Editors: Robert Brown, University of Waterloo ○ Cecil Bykerk, Mutual of Omaha ○ Ruy Cardoso, …

Can Utility-Maximization Models Assist With Retirement Planning?, Zaki Khorasanee

Journal of Actuarial Practice (1993–2006)

Utility-maximization models for optimizing portfolio choices can be subdivided into two classes: those based on maximizing the expected utility of lifetime consumption and those based on maximizing the expected utility of retirement wealth. It is argued that the first type of model, which optimizes both saving and investment decisions, is difficult to apply in practice because of inadequate (or unreliable) information about individual preferences. Although the second type of model only optimizes investment decisions, it is of greater practical value because fewer data on individual preferences are required. The second type of model is used to derive formulae for the …

Some Comments On The Pricing Of An Exotic Excess Of Loss Treaty, Jean-Francois Walhin

Journal of Actuarial Practice (1993–2006)

This paper uses a multivariate analog of Panjer's algorithm to develop a method for pricing a complex excess of loss treaty. The treaty is such that some layers inure to the benefit of other layers. The structure of this treaty is discussed. Numerical examples are provided.

Communicating Effectively With Words, Numbers, And Pictures: Drawing On Experience, Karolina Duklan, Michael A. Martin

Journal of Actuarial Practice (1993–2006)

In this paper, we discuss techniques for developing effective communication skills, focusing in particular on technical writing, the use of graphics, and presentation. The key principles of effective communication that we propose to actuaries are as follows:

• Identify your audience and consider their needs and abilities;

• Focus on substantive content;

• Choose appropriate communication tools;

• Use language that is simple, concrete, and familiar;

• Integrate text, numbers, and graphics;

• Respond to information complexity creatively.

We focus in particular on the use of graphics as a communications tool as they are an efficient and potentially highly effective …

Further Remarks On Risk Sources Measuring: The Case Of A Life Annuity Portfolio, Mariarosaria Coppola, Emilia Di Lorenzo, Marilena Sibillo

Journal of Actuarial Practice (1993–2006)

The paper considers a model that allows the actuary to measure the riskiness connected to the randomness of projected mortality tables in evaluating a portfolio of life annuities, obtaining a measure to reflect the risk associated with the randomness of the projection. The coherence of the risk parameters with the specific nature of the considered risk sources is also discussed. Numerical examples illustrate the results, showing the importance of the risk components in terms of the number of policies and comparing measure tools obtained by means of two procedures.

A Note On The Parallelogram Method For Computing The On-Level Premium, David P.M. Scollnik, Wai Man Sara Lau

Journal of Actuarial Practice (1993–2006)

This paper discusses the differences appearing in the descriptions of the parallelogram method for the determination of earned premium at current rate levels given by McClenahan (1996) and Brown and Gottlieb (2001). It observes that the former is consistent with the method of extending exposures while the latter is not. An illustration is provided. This paper also discusses two other approaches to the determination of the earned premium.

Dynamic Funding And Investment Strategy For Defined Benefit Pension Schemes: A Model Incorporating Asset-Liability Matching Criteria, Shih-Chieh Chang, Cheng-Hsien Tsai, Chia-Jung Tien, Chang-Ye Tu

Journal of Actuarial Practice (1993–2006)

This paper studies the dynamic funding policy and investment strategy for defined benefit pension plans using one of the most comprehensive dynamic pension models to date. The model includes three investable assets: one risk free and two risky. The optimal plan decisions are formulated as a stochastic control problem that is solved using dynamic programming. The objective function uses performance measures to take into account the stability and solvency of the plan. The model is then applied to a Taiwanese pension.

Fitting Loss Distributions In The Presence Of Rating Variables, Farrokh Guiahi

Journal of Actuarial Practice (1993–2006)

This paper focuses on issues and methodologies for fitting alternative statistical models-parametric probability distributions-to samples of insurance loss data. The interactions of loss distributions, deductibles, policy limits, and rating variables in the context of fitting distributions to losses are discussed. Fitted loss distributions serve an important function in pricing insurance products. The methodology developed in this paper is applied to a sample of insurance loss data that has the lognormal as the underlying loss distribution.

Linear Empirical Bayes Estimation Of Survival Probabilities With Partial Data, Mostafa Mashayekhi

Journal of Actuarial Practice (1993–2006)

In this paper we consider linear empirical Bayes estimation of survival probabilities with partial data from right-censored and possibly left-truncated observations. Such data are produced by studies in which the exact times of death are not recorded and the length of time that each subject may be under observation cannot exceed one unit of time. We obtain asymptotically optimal linear empirical Bayes estimators, with respect to the squared error loss function, under the assumption that the probability of death under observation in a unit time interval is proportional to the length of observation. This assumption is sometimes implied by Balducci's …

A Sensitivity Analysis Of The Premiums For A Permanent Health Insurance (Phi) Model, Ben D. Rickayzen

Journal of Actuarial Practice (1993–2006)

This paper presents an analysis of the parameters used in a multi-state model for permanent health insurance (PHI). The model is a simplification of that used in the United Kingdom. To avoid using duration dependent probabilities, the model splits the sick state into several sub-states to act as a proxy for duration spent in a particular state. This enables a Markov approach to be adopted. Lapses are incorporated within the model, and the net premium for a particular policy is tested for sensitivity to the various parameters used, including their interaction with the lapse rate. One of our conclusions is …

Controlling The Solvency Interaction Among A Group Of Insurance Companies, Alexandros Zimbidis, Steven Haberman

Journal of Actuarial Practice (1993–2006)

Pooling of risks is an efficient risk management technique used by large employee benefit schemes of multinational companies to self-insure their retirement and other benefit obligations. This technique forms a basis for formulating a general control theoretic model for the interaction between insurance companies within a pooling network. The objective of these insurance companies is to avoid insolvency yet maintain stable premium and surplus processes. A general control system of equations that is used as a model for the interaction of m insurance companies within the network is first analyzed. An analytic solution is provided. Questions concerning the stability and …

Exponential Bonus-Malus Systems Integrating A Priori Risk Classification, Llufs Bermudez, Michel Denuit, Jan Dhaene

Journal of Actuarial Practice (1993–2006)

This paper examines an integrated ratemaking scheme including a priori risk classification and a posteriori experience rating. In order to avoid the high penalties implied by the quadratic loss function, the symmetry between the overcharges and the undercharges is broken by introducing parametric loss functions of exponential type.

Premium Earning Patterns For Multi-Year Policies With Aggregate Deductibles, Thomas Struppeck

Journal of Actuarial Practice (1993–2006)

MUlti-year policies with large aggregate deductibles or multiple triggers raise some interesting issues about the correct amount of unearned premium reserve that a company should carry. Examples in this paper illustrate some of the difficulties that arise when trying to establish such reserves. The basic approach taken here is that the pure premium portion of the unearned premium reserve should always be adequate to cover the remaining risk. This approach, however, can lead to some unusual and controversial earning patterns; there are even situations where a negative premium is earned. In addition, the earning pattern for a particular loss scenario …

Analyzing Management Fees Of Pension Funds: A Case Study Of Mexico, Tapen Sinha

Journal of Actuarial Practice (1993–2006)

Though the rates of return for public pension funds have been high over the past two decades, one critical aspect of the financing of this type of fund is often overlooked: high management fees. As a result, the rates of return for workers who have invested in these funds have not necessarily been high. Management fees charged on pension funds in Mexico result in a leakage of funds in the order of 20-30% of the fund. That is, the amount at retirement would have been 20-30% higher had there been no fees. A model is developed that includes all the …

Journal Of Actuarial Practice, Volume 9 (2001), Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

(The complete issue, including) ARTICLES

Analyzing Management Fees of Pension Funds: A Case Study of Mexico • Tapen Sinha 5

Premium Earning Patterns for Multi-Year Policies with Aggregate Deductibles • Thomas Struppeck 45

Exponential Bonus-Malus Systems Integrating A Priori Risk Classification • Lluis Benmidez, Michel Denuit, and Jan Dhaene 67

Fitting Loss Distributions in the Presence of Rating Variables • Farrokh Guiahi 97

Linear Empirical Bayes Estimation of Survival Probabilities with Partial Data • Mostafa Mashayekhi 131

Controlling the Solvency Interaction Among a Group of Insurance Companies • Alexandros Zimbidis and Steven Haberman 151

A Sensitivity Analysis of the Premiums …

Journal Of Actuarial Practice, Volume 8, Nos. 1 And 2 (2000) -- Masthead & Contents, Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

Contents

Editorial Policy: Topics suitable for this journal include AIDS, annuity products, asset-liability matching, cash-flow testing, casualty rate making, credibility theory, credit insurance, disability insurance, expense analysis, experience studies, FASB issues, financial reporting, group insurance, health insurance, individual risk taking, insurance regulations, international issues, investments, liability insurance, loss reserves, marketing, pensions, pricing issues, product development, reinsurance, reserving issues, risk-based capital, risk theory, social insurance, solvency issues, taxation, valuation issues, and workers' compensation

Review Process

Editor - Colin Ramsay, University of Nebraska

Associate Editors: Robert Brown, University of Waterloo ○ Cecil Bykerk, Mutual of Omaha ○ Ruy Cardoso, …

Journal Of Actuarial Practice, Volume 8, Nos. 1 And 2 (2000), Colin Ramsay , Editor

Journal of Actuarial Practice (1993–2006)

Complete volume, includes ARTICLES:

Realistic Pension Funding: A Stochastic Approach • Shih-Chieh Chang 5

Risk Sources in a Life Annuity Portfolio: Decomposition and Measurement Tools • Mariarosaria Coppola, Emilia Di Lorenzo, and Mari/ena Sibillo . .43

A Comparative Study of the Performance of Loss Reserving Methods through Simulation • Prakash Narayan and Thomas Warthen 63

Concentration in the Property and Liability Insurance Market by Line of Insurance • Edward Nissan and Regina Caveny 89

Safe-Side Requirements in Life Insurance: A Corporate Perspective • Annamaria Olivieri and Ermanno Pitacco 115

Actuarial Analysis of Retirement Income Replacement Ratios • Robert Keng Heong …

Modeling Corporate Bond Default Risk: A Multiple Time Series Approach, Wai-Sum Chan

Journal of Actuarial Practice (1993–2006)

A multiple time series approach is used to forecast the short-term u.s. corporate bond default level. These time series have two auxiliary economic variables: U.S. price inflation and U.S. GNP growth rate. Actual U.S. data from the turn of the century to the present are used to estimate the parameters of multivariate time series model. Diagnostic checks are performed to examine adequacy of the model. The model's forecast for the aggregate U.S. bond default level in 2000-2001 are 0.42% and 0.56%, respectively, while the forecast for the speculative-grade default rate in 2000 is 3.6%, which is more pessimistic than some …

Actuarial Analysis Of Retirement Income Replacement Ratios, Robert Keng Heong Lian, Emiliano A. Valdez, Chan Kee Low

Journal of Actuarial Practice (1993–2006)

A measure of level of post-retirement standard of living is the replacement ratio, i.e., percentage of final salary received as annual retirement income derived from savings. The replacement ratio depends on many factors including salary, salary increases, investment returns, and post-retirement mortality. Elementary life contingencies techniques are used to develop a replacement ratio formula and analyze its sensitivity to these factors.

Life Contingencies With Stochastic Discounting Using Moving Average Models, Steven Haberman, Russell Gerrard, Dimitrios Velmachos

Journal of Actuarial Practice (1993–2006)

This paper offers simplified procedures for calculating moments of functions in life contingencies when the random force of interest is modeled using an unconditional moving average process of order q, MA(q). It extends the MA(l) model that has been used for stochastic discounting. Using the more general MA(q) model allows actuaries to better capture the auto correlation between successive interest rates in a time series.